Low current waveguide free electron lasers (FELs) operating in the spectrum from microwave to the infrared have a distinct advantage of small size and low cost? important for realistic applications in medicine and industry, One of the long-term objectives in the development of these compact FELs is to reduce the necessary electron beam voltage for a strong FEL interaction at a given frequency. In this paper, we consider a longitudinal interaction between the longitudinal component of the electron beam's undulating motion and the longitudinal electric field of TM modes of the waveguide electromagnetic wave. A small signal analysis is presented to study the longitudinal interaction mechanism. It is shown that the electron beam voltage can be reduced considerably from what is needed in the conventional transverse interaction of the electron beam with TE modes at the same frequency. In a design example of an X-band FEL amplifier, this reduction is found to be more than half. Gain calculation suggests that with a reasonable wiggler field such a. longitudinal interaction leads to a sizeable FEL amplification of TM modes. (C) 1997 Elsevier Science B.V.